Question

Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.

a.18 x minus 15 = 72
b.50 x minus 25 = 72
c.18 x minus 9 = 72
d.3 (6 x minus 3) = 72
e.x=4.5

Answer 1

C, D and E

Explanation:

Given equation:

`\frac35(30x-15)=72`

Use the distributive law
`a(b-c)=ab-ac`:

`\implies \frac35\cdot30x- \frac35\cdot15=72`

`\implies \frac{3 \cdot30}5x- \frac{3 \cdot15}5=72`

`\implies \frac{90}5x- \frac{45}5=72`

`\implies 18x- 9=72` ← option c

Factor out common term 3:

`\implies 3(6x- 3)=72` ← option d

Solve
`18x- 9=72`:

`\implies 18x- 9+9=72+9`

`\implies 18x=81`

`\implies (18x)/(18)=(81)/(18)`

`\implies x=4.5` ← option e